Stars Thursday, February 28
Thu, Feb 28: Stars Tue, Mar 4: PlanetsProblem Set #7 due Thu, Mar 6: Past & FutureProblem Set #7 returned Tue, Mar 11, 1:30 pmFinal Exam
What is a star? Examples of stars: Sun Betelgeuse
Pleiades: known traditionally as the “seven sisters” (6 bright stars, 1 fainter) With his telescope, Galileo saw many more stars.
Average density of ordinary matter in the universe = 0.04ρcrit = 3.6 × 10-28 kg/m3 Density of Sun = 1400 kg/m3 =4 quadrillion quadrillion × average Stars are lumps of ordinary matter compressed to small size and high density.
What is a star? A luminous ball of gas powered by nuclear fusion in its interior.
“Why do stars shine?” Stars are dense (Sun is 40% denser than liquid water). Stars are opaque (because they’re made of ionized gas). Stars are hot (surface temperatures > 2000 Kelvin).
Flashback slide! Hot, dense, opaque objects emit light! Today, we call hot, dense, opaque objects that emit light “stars”.
Question: Why do stars shine? Short answer: Stars shine because they are hot. Follow-up question: Why don’t stars cool down?
There’s a continuous fossil record of life on Earth for over 3 billion years. Sun’s luminosity can’t have been wildly variable – if it had, life would have scorched or frozen.
Sun must have an interior power source to replace the energy carried away by photons. What’s the power source? The Sun’s mostly hydrogen – what about burning hydrogen?
2 H + O → H2O + energy Burning 1 kg of hydrogen releases 1.4 × 108 joules of energy. Sun’s mass = 2 × 1030 kg. (1.4 × 108 joules/kg) × (2 × 1030 kg) = 2.8 × 1038 joules
The Sun throws away energy at a rate Lsun = 3.9 × 1026 watts = 3.9 × 1026 joules/sec. Time to “burn up” the Sun = 2.8 × 1038 joules / 3.9 × 1026 joules/sec = 7.2 × 1011 seconds = 23,000 years Absurdly short time!
We need a power source that gives us more bang for the buck (more joules for the kilogram…) The Sun’s mostly hydrogen – what about nuclear fusion, converting hydrogen into helium?
4 H → He + a lot of energy Fusing 1 kg of hydrogen into helium releases 6.3 × 1014 joules of energy. That’s 4.5 million times what you’d get byburning the hydrogen. Sun’s hydrogen supply adequate for billions, not thousands, of years.
If nuclear fusion is such a great energy source, why don’t we all have “Mr. Fusion” units?
proton positron Fusion inside the Sun neutron neutrino proton photon Helium
The fusion chain starts with combining two protons. Protons are positively charged; overcoming their electrostatic repulsion requires high speeds. T > 10 million Kelvin.
Energy is generated in the Sun’s hot core. Energy is radiated from the Sun’s surface, 700,000 km away. How does the energy get from the core to the surface?
Photons are good at carrying energy from point A to point B. A B If the Sun were transparent, photons could travel from its center to its surface in 2.3 seconds.
The Sun is not transparent. Photons travel only an inch before being scattered in a random direction. It takes 200,000 years (on average) for light to stumble its way to the surface.
Galaxies form because ordinary matter can cool down (by emitting photons) and fall to the center of dark halos. Why do galaxies curdle into tiny stars, instead of remaining as homogenous gas clouds?
Look at where stars are forming now. In the Whirlpool Galaxy, we see newly formed stars in dense, cold molecular clouds.
In regions where the gas is cooler and denser than elsewhere, hydrogen forms molecules (H2). These cool, dense regions are thus called “molecular clouds”.
Consider a small, dense molecular cloud. Mass = 1 Msun Radius = 0.1 pc = 4,000,000 Rsun Temperature = 10 Kelvin = Tsun/580
Molecular clouds are usually stable; but if you hit them with a shock wave, they start to collapse gravitationally. Once the collapse is triggered, it “snowballs”. shock waves
Once gravity has reduced the radius of the cloud by a factor of 4,000,000, it’s the size of a star. Why doesn’t the molecular cloud collapse all the way to a black hole?
Escape speed from molecular cloud≈ 0.3 km/sec Escape speed from star≈ 600 km/sec Escape speed from black hole = 300,000 km/sec
When the gas temperature is high enough (T ≈ 10 million Kelvin), nuclear fusion begins! As the gas of the molecular cloud is compressed, it becomes denser. As the gas is compressed, it also becomes hotter.
Nuclear fusion keeps the central temperature and pressure of the star at a constant level. The star is static (not contracting or expanding) because it’s in hydrostatic equilibrium.
Hydrostatic equilibrium = a balance between gravity and pressure. Pressure increases as you dive deeper into the ocean: pressure increases as you dive deeper into the Sun.
For a fish in the ocean, pressure creates a net upward force, gravity creates a downward force. The fish is in hydrostatic equilibrium.
For gas in the Sun, pressure creates a net outward force, gravity creates a inward force. The Sun is in hydrostatic equilibrium.
The Sun is like a fat guy on an inflatable chair. fusion energy gravity pressure
Hydrostatic equilibrium tends to be very stable. Put a six-pack on fat guy’s lap. Gravitational force increases. Gas in chair is compressed. Upward pressure force increases.
Hydrostatic equilibrium is common throughout the universe. Sun is in hydrostatic equilibrium. Oceans are. Earth’s atmosphere is. Earth’s interior is. Fat guys in inflatable chairs are.
Tuesday’s Lecture: Formation and Evolution of Planets Reading: none